Paying down debt is arguably the most valuable step you can take toward accumulating savings. As long as debt payments are draining a sum from every paycheck, you aren't going to have the funds for a significant saving program. And because the interest on your debt is always going to be higher than what you'll earn with a traditional savings account, reducing debt is the best way to put any extra money to work. Once you've cleared away your debt, you can put the funds you were formerly paying each month on a loan into your savings account.
Avoid the habit of just carrying debt. For example, if you pay only the minimum on your credit card, it will take you years to pay off what you owe. And credit card interest is sky high. Your goal should be to carry no balance on your credit card.
But at the same time, that doesn't mean all of your extra income should go into debt reduction. Even if you owe money, you need a savings account. In addition to a rainy day fund for emergencies, you need to put away money for upcoming expenses like insurance premiums. Draw up a budget that lets you pay down debt as quickly as quickly as possible and accumulate some savings as well.